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  1. Andrew Bacon (2013). Quantificational Logic and Empty Names. Philosophers' Imprint 13 (24).
    The result of combining classical quantificational logic with modal logic proves necessitism – the claim that necessarily everything is necessarily identical to something. This problem is reflected in the purely quantificational theory by theorems such as ∃x t=x; it is a theorem, for example, that something is identical to Timothy Williamson. The standard way to avoid these consequences is to weaken the theory of quantification to a certain kind of free logic. However, it has often been noted that in order (...)
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  2. John Bacon (1982). First-Order Logic Based on Inclusion and Abstraction. Journal of Symbolic Logic 47 (4):793-808.
  3. Ermanno Bencivenga (2002). Free Logics. In D. M. Gabbay & F. Guenthner (eds.), Handbook of Philosophical Logic, 2nd Edition. Kluwer 147--196.
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  4. V. A. Bocharov (1983). Subject-Predicate Calculus Free From Existential Import. Studia Logica 42 (2-3):209 - 221.
    Two subject-predicate calculi with equality,SP = and its extensionUSP =, are presented as systems of natural deduction. Both the calculi are systems of free logic. Their presentation is preceded by an intuitive motivation.It is shown that Aristotle's syllogistics without the laws of identitySaP andSiP is definable withinSP =, and that the first-order predicate logic is definable withinUSP =.
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  5. Newton C. A. da Costa & Otavio Bueno (1999). Quasi-Truth, Supervaluations and Free Logic. History and Philosophy of Logic 20 (3-4):215-226.
    The partial structures approach has two major components: a broad notion of structure (partial structure) and a weak notion of truth (quasi-truth). In this paper, we discuss the relationship between this approach and free logic. We also compare the model-theoretic analysis supplied by partial structures with the method of supervaluations, which was initially introduced as a technique to provide a semantic analysis of free logic. We then combine the three formal frameworks (partial structures, free logic and supervaluations), and apply the (...)
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  6. D. M. Gabbay & F. Guenthner (eds.) (2002). Handbook of Philosophical Logic, 2nd Edition. Kluwer.
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  7. Roderic A. Girle (1974). Possibility Pre-Supposition Free Logics. Notre Dame Journal of Formal Logic 15 (1):45-62.
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  8. Jan Heylen (2016). Russell's Revenge: A Problem for Bivalent Fregean Theories of Descriptions. Pacific Philosophical Quarterly 97 (1):n/a-n/a.
    Fregean theories of descriptions as terms have to deal with improper descriptions. To save bivalence various proposals have been made that involve assigning referents to improper descriptions. While bivalence is indeed saved, there is a price to be paid. Instantiations of the same general scheme, viz. the one and only individual that is F and G is G, are not only allowed but even required to have different truth values.
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  9. Srećko Kovač & Kordula Świętorzecka (2015). Gödel's "Slingshot" Argument and His Onto-Theological System. In Kordula Świętorzecka (ed.), Gödel's Ontological Argument: History, Modifications, and Controversies. Semper 123-162.
  10. Siu-Fan Lee (2009). Fregean Free Logics. Philosophical Researches (Dec):123-129.
    This paper asks which free logic a Fregean should adopt. It examines options within the tradition including Carnap’s (1956) chosen object theory, Lehmann’s (1994, 2002) strict Fregean free logic, Woodruff’s (1970) strong table about Boolean operators and Bencivenga’s (1986, 1991) supervaluational semantics. It argues for a neutral free logic in view of its proximity towards explaining natural languages. However, disagreeing with Lehmann, it claims a Fregean should adopt the strong table based on Frege’s discussion on generality. Supervaluation uses strong table (...)
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  11. Carl J. Posy (1982). A Free IPC is a Natural Logic: Strong Completeness for Some Intuitionistic Free Logics. Topoi 1 (1-2):30-43.
    IPC, the intuitionistic predicate calculus, has the property(i) Vc(A c /x) xA.Furthermore, for certain important , IPC has the converse property (ii) xA Vc(A c /x). (i) may be given up in various ways, corresponding to different philosophic intuitions and yielding different systems of intuitionistic free logic. The present paper proves the strong completeness of several of these with respect to Kripke style semantics. It also shows that giving up (i) need not force us to abandon the analogue of (ii).
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